In a game of lawn bowls, the object is to bowl a biased ball so that it gets as close as possible to a smaller white ball called a jack. During a game, a player will sometimes bowl a ball quite quickly so that it travels in a straight line in order to displace an opponent’s ‘guard balls’. In a particular game, player X has 2 guard balls close to the jack. The coordinates of the jack are (0, 0) and the coordinates of the guard balls are A (−1, 4/5) and B (−1/2, 57/40). Player Y bowls a ball so that it travels in a straight line toward the jack. The ball is bowled from position S, which has coordinates (–30, 24).

Question

a. Will player Y displace one of the guard balls? If so, which one?
If you plot the points onto an online graph, it doesn't look like any of the guard balls will be displaced if the ball is bowled straight from 'S' to the jack (0,0)

b. Due to bias, the displaced guard ball is knocked so that it begins to travel in a straight line (at right angles to the path found in part a).
Find the equation of the line of the guard ball.

c. Show that guard ball A is initially heading directly toward guard ball B.

d. Given its initial velocity, guard ball A can travel in a straight line for 1 metre before its bias affects it path. Calculate and explain whether guard ball A will collide with guard ball B

Answer 1

This depends on the size of the balls.
Also, there is no way a ball can be hit so it takes off at a right angle.

Fix up the question, and maybe answers can be determined.

at any rate, to determine the equation of the line, its slope is the negative reciprocal of the incoming line; now you have a slope and a point, so use the point-slope form of the line.